We need to find a range of values to appropriately label events of concern.
We use,
as a surrogate to label a concern event.
Conclusions:
where \(Pc\_warn\) is the \(\text{Collision Probability}\) that triggers a warning.
We need to evaluate warning thresholds by examining the trade space between risk aversion and tolerance.
We have the following working definitions:
\(\text{Concern Event} := \text{Collision Probability} >= 1\text{e-}5 \text{ and days to TCA < 1 day}\),
\(\text{False Negative (FN)} := \text{Number of Concern Events that did not trigger a warning at 5 days to TCA}\), and
\(\text{False Positive (FP)} := \text{Number of false alarms, where warned events at 5 days to TCA did not become Concern Events}\).
We can now explore how the warning threshold effects the \(\text{FP}\) and \(\text{FN}\).
Hovering over the plot, we see that the warning threshold decreases as FN decreases and as FP increases. In this case, the more severe mistake is FN (not warning for a concern event), which is our Type II error. The FP (false alarm, Type I error) has much lower rates because of the high number of events with Collision Probabilities falling below \(1\text{e-}5\) within one day to TCA.
We recommend this chart to inform warning thresholds for five days to TCA, for concern events previously defined.